High Precision Judgement Method for Milling Stability Based on Bernoulli Distribution and Hybrid Drive Model

doi:10.3901/JME.2024.11.318

Abstract

Abstract: Milling chatter seriously affects workpiece surface quality and production efficiency. It is very important to identify milling stability domain accurately for suppressing chatter and improving production efficiency. At present, the stability of milling system is generally judged according to the spectral radius of eigenvalue of state transition matrix is less than 1. Due to the uncertainty in milling and hammering experiments, there exist errors to affect milling system attribute parameters and in turn, greatly affect the judgment results of stability. Therefore, by studying the probabilistic characteristics of chatter stability in milling process, a correction method of SLD (stability lobe diagram) based on attribute parameter optimization is established. Firstly, a milling stability judgment model is established by using Cotes integral method and Floquet theory. Secondly, the stability judgment model is equivalent described by Bernoulli distribution probability function. The correction functions of attribute parameters are proposed according to Bernoulli distribution law of stability judgment results. Finally, the golden section method and genetic algorithm based on the neural network are proposed to optimize the attribute parameters. The experimental results show that the stability accuracy of the proposed method for a single lobe is improved from 69.77% to 93.02% whereas the accuracy of the whole SLD is improved from 73.73% to 87.29%.

Key words: chatter, Cotes integration, stability lobe diagram, Bernoulli distribution, data driven method, optimization

CLC Number:

TH161

TAN Zhipu, QIN Guohua, LOU Weida, WU Zhuxi. High Precision Judgement Method for Milling Stability Based on Bernoulli Distribution and Hybrid Drive Model[J]. Journal of Mechanical Engineering, 2024, 60(11): 318-331.

References

[1] ALTINTAS Y,WECK M.Chatter stability of metal cutting and grinding[J].CIRP Annals,2004,53:619-642.
[2] TOBIAS S A.Machine tool vibration research[J].International Journal of Machine Tool Design and Research,1961,1:1-14.
[3] SCHMITZ T L,SMITH K S.Machining dynamics[M].Boston,MA:Springer US,2009.
[4] KURDI M H,SCHMITZ T L,HAFTKA R T,et al.A numerical study of uncertainty in stability and surface location error in high-speed milling[C]//Proceedings of the ASME 2005 International Mechanical Engineering Congress and Exposition.Manufacturing Engineering and Materials Handling,Parts A and B.Orlando,Florida,USA.November 5-11,2005:387-395.
[5] ZHANG X M,ZHU L M,ZHANG D,et al.Numerical robust optimization of spindle speed for milling process with uncertainties[J].International Journal of Machine Tools and Manufacture,2012,61:9-19.
[6] HUANG X Z,HU M W,ZHANG Y M,et al.Probabilistic analysis of chatter stability in turning[J].International Journal of Advanced Manufacturing Technology,2016,87:3225-3232.
[7] TOTIS G.RCPM-a new method for robust chatter prediction in milling[J].International Journal of Machine Tools and Manufacture,2009,49:273-284.
[8] BUDAK E,ALTINTAS Y.Analytical prediction of chatter stability in milling-part I:General formulation[J].Journal of Dynamic Systems,Measurement,and Control,1998,120:22-30.
[9] INSPERGER T,STÉPÁN G.Semi-discretization method for delayed systems[J].International Journal for Numerical Methods in Engineering,2002,55:503-518.
[10] DING Y,ZHU L M,ZHANG X J,et al.A full-discretization method for prediction of milling stability[J].International Journal of Machine Tools and Manufacture,2010,50:502-509.
[11] QIN C J,TAO J F,LIU C L.Stability analysis for milling operations using an Adams-Simpson-based method[J].International Journal of Advanced Manufacturing Technology,2017,92:969-979.
[12] JI Y J,WANG X B,LIU Z B,et al.An updated full-discretization milling stability prediction method based on the higher-order Hermite-Newton interpolation polynomial[J].International Journal of Advanced Manufacturing Technology,2018,95:2227-2242.
[13] LI W T,WANG L P,YU G.An accurate and fast milling stability prediction approach based on the Newton-Cotes rules[J].International Journal of Mechanical Sciences,2020,177:105469.
[14] DONG X F,QIU Z Z.Stability analysis in milling process based on updated numerical integration method[J].Mechanical Systems and Signal Processing,2020,137:106435.
[15] SCHMITZ T L,DONALSON R R.Predicting high-speed machining dynamics by substructure analysis[J].CIRP Annals,2000,49:303-308.
[16] ÖZŞAHIN O,ÖZGÜVEN H N,BUDAK E.Analysis and compensation of mass loading effect of accelerometers on tool point FRF measurements for chatter stability predictions[J].International Journal of Machine Tools and Manufacture,2010,50:585-589.
[17] ÖZŞAHIN O,ALTINTAS Y.Prediction of frequency response function (FRF) of asymmetric tools from the analytical coupling of spindle and beam models of holder and tool[J].International Journal of Machine Tools and Manufacture,2015,92:31-40.
[18] EYNIAN M.In-process identification of modal parameters using dimensionless relationships in milling chatter[J].International Journal of Machine Tools and Manufacture,2019,143:49-62.
[19] DANG J W,ZHANG W H,YANG Y,et al.Cutting force modeling for flat end milling including bottom edge cutting effect[J].International Journal of Machine Tools and Manufacture,2010,50:986-997.
[20] KARANDIKAR J,HONEYCUTT A,SCHMITZ T,et al.Stability boundary and optimal operating parameter identification in milling using Bayesian learning[J].Journal of Manufacturing Processes,2020,56:1252-1262.
[21] POSTEL M,BUGDAYCI B,WEGENER K.Ensemble transfer learning for refining stability predictions in milling using experimental stability states[J].International Journal of Advanced Manufacturing Technology,2020,107:4123-4139.
[22] CHEN G X,LI Yi G,LIU X,et al.Physics-informed Bayesian inference for milling stability analysis[J].International Journal of Machine Tools and Manufacture,2021,167:103767.
[23] LOU W D,QIN G H,ZUO D W.Investigation on Cotes-formula-based prediction method and its experimental verification of milling stability[J].Journal of Manufacturing Processes,2021,64:1077-1088.
[24] TOTIS G,SORTINO M.Polynomial chaos-kriging approaches for an efficient probabilistic chatter prediction in milling[J].International Journal of Machine Tools and Manufacture,2020,157:103610.
[25] CHERUKURI H,PEREZ-BERNABEU E,SELLES M,et al.Machining chatter prediction using a data learning model[J].Journal of Manufacturing and Materials Processing,2019,3(2):3020045.
[26] CUEVAS E,ENRÍQUEZ L,ZALDÍVAR D,et al.A selection method for evolutionary algorithms based on the golden section[J].Expert Systems with Applications,2018,106:183-196.
[27] BANAEI A,ALAMATIAN J,ZIA-TOHIDI R.Active control of structures using genetic algorithm with dynamic weighting factors using in the constrained objective function[J].Structures,2022,47:189-200.
[28] HAJDU D,BORGIOLI F,MICHIELS W,et al.Robust stability of milling operations based on pseudospectral approach[J].International Journal of Machine Tools and Manufacture,2020,149:103516.